Question

Solutions

When you try to do this question, try changing it into \(3^n\)/\(4^n\).

After, try expanding the summation into \((\frac{3}{4} + (\frac{3}{4})^2 + (\frac{3}{4})^3 + ... )\).

Next, you factor common multiples out. \(= \frac{3}{4}(1+\frac{3}{4}+(\frac{3}{4})^2+...)\)

Then, you find values a and r. In this case, a is \(\frac{3}{4}\) and r is also \(\frac{3}{4}\).

In the end, you substitute a and r into the equation \(\frac{a}{1 - r}\).

This results in

But since \(3^{n+1} = 3 \cdot 3^n\), \(3 \times 3 = 9\).

The answer is \(9\).

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